the value of 3cosA+4sinA lie betweena)-7&7b)-25&25c)-5&5

Any such question has the formula of min as -root(a^2+b^2) and max as root(a^2+b^2). Where a,b are found by comparing asinx+bcosx

 

Proof of this is by multiplying and dividing by root(a^2+b^2)

 

Then make it as sinxcosa+cosxsina where a is the other angle.

 

For trignometry a trig (bx+c) +d is the general form where a is amplitude. In this case if you convery to this form then a=root(a^2+b^2) thus max and min is root(a^2+b^2) and -root(a^2+b^2)